Integrable pseudopotentials related to generalized hypergeometric functions

Abstract

We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of integrable (1+1)-dimensional hydrodynamic type systems is also generated by our pseudopotentials.

Latex, 28 pages, new material on integrable 3-dimensional hydrodynamic type systems is added

References in corpus (5)

• On integrability of (2+1)-dimensional quasilinear systems
• A family of (2+1)-dimensional hydrodynamic type systems possessing pseudopotential
• Second order quasilinear PDEs and conformal structures in projective space
• Integrable Lagrangians and modular forms
• Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian

Cited by in corpus (2)

• Integrable (2+1)-dimensional systems of hydrodynamic type
• Classification of integrable hydrodynamic chains